The far-right protesters, some waving Confederate flags, carrying shields and wearing helmets, are angry about the planned removal of a statue of General Robert E Lee from Charlottesville.

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Media captionPresident Trump condemned the “hatred and violence” in Charlottesville

Gen Lee commanded the pro-slavery Confederate forces in the US Civil War of 1861-65.

The New York Times reports that some of them were chanting “You will not replace us,” and “Jew will not replace us.”

Anti-racism organisations such as Black Lives Matter also held marches.

President Donald Trump condemned “in the strongest possible terms this egregious display of hatred, bigotry, and violence on many sides”.

“The hate and the division must stop right now,” he told reporters, speaking in New Jersey, where he is on a working holiday. “We have to come together as Americans with love for our nation.”

At the scene: Bottles thrown

By Joel Gunter, BBC News, Charlottesville

There were very violent scenes at Emancipation Park and it took some time for the police to intervene.

Both sides were throwing bottles and rocks and using pepper spray.

The far-right protesters were a mix of different groups with shields and batons and the declaration of a state of emergency seemed to have had a significant impact on them, as they started to dissipate.

Shiquan Rah, a 21-year-old demonstrator who had joined the counter-protest, said about the far-right groups: “These people don’t have a message, their message is hate and violence. This is a spiritual war we’re in.

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Media captionThe BBC’s Joel Gunter describes the clashes, where groups were armed with shields and batons

Virginia Governor Terry McAuliffe urged calm tweeting: “The acts and rhetoric in #Charlottesville over past 24 hours are unacceptable [and] must stop. A right to speech is not a right to violence.”

Charlottesville Mayor Mike Signer had earlier called the rally a “parade of hatred, bigotry, racism and intolerance”.

US Civil War and alt-right links

1861-65 US Civil War between the northern and southern states was principally caused by slavery

Southern Confederate forces, which backed slavery, eventually surrendered to Union army and slavery was abolished

A number of cities have grappled with Confederate symbols that still exist today, with flags and monuments becoming key venues for alt-right groups in recent months

Supporters say Confederate symbols represent freedom and liberty, but opponents say their roots are in slavery

The alt-right is a disparate group of provocateurs who hate political correctness and love Donald Trump, but critics say they are bigoted white nationalists

On Friday, the white nationalists held lit torches – which some observers described as a reference to the Ku Klux Klan – and chanted “White lives matter” as they marched through the University of Virginia in the city.

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Members of a white nationalist group were armed and wearing militia uniforms

Charlottesville is considered a liberal college town – and 86% of the county voted for Hillary Clinton in last year’s presidential elections.

However, the town has become a focal point for white nationalists after the city council voted to remove the statue of Gen Lee.

Some observers also argue that Mr Trump’s election to the White House re-energised the far right across the US.